The Solvability and Optimal Controls for Some Fractional Impulsive Equations of Order 1< α<2
We study the existence of solutions and optimal controls for some fractional impulsive equations of order 1< α<2. By means of Gronwall’s inequality and Leray-Schauder’s fixed point theorem, the sufficient condition for the existence of solutions and optimal controls is presented. Finally, an e...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/142067 |
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| _version_ | 1832558744227020800 |
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| author | Xianghu Liu Zhenhai Liu Maojun Bin |
| author_facet | Xianghu Liu Zhenhai Liu Maojun Bin |
| author_sort | Xianghu Liu |
| collection | DOAJ |
| description | We study the existence of solutions and optimal controls for some fractional impulsive equations of order 1< α<2. By means of Gronwall’s inequality and Leray-Schauder’s fixed point theorem, the sufficient condition for the existence of solutions and optimal controls is presented. Finally, an example is given to illustrate our main results. |
| format | Article |
| id | doaj-art-9e0f03c5f2124c95b8de0616d030cb9e |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-9e0f03c5f2124c95b8de0616d030cb9e2025-02-03T01:31:37ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/142067142067The Solvability and Optimal Controls for Some Fractional Impulsive Equations of Order 1< α<2Xianghu Liu0Zhenhai Liu1Maojun Bin2School of Mathematics and Statistics, Central South University, Changsha, Hunan 410075, ChinaCollege of Sciences, Guangxi University for Nationalities, Nanning, Guangxi 530006, ChinaCollege of Sciences, Guangxi University for Nationalities, Nanning, Guangxi 530006, ChinaWe study the existence of solutions and optimal controls for some fractional impulsive equations of order 1< α<2. By means of Gronwall’s inequality and Leray-Schauder’s fixed point theorem, the sufficient condition for the existence of solutions and optimal controls is presented. Finally, an example is given to illustrate our main results.http://dx.doi.org/10.1155/2014/142067 |
| spellingShingle | Xianghu Liu Zhenhai Liu Maojun Bin The Solvability and Optimal Controls for Some Fractional Impulsive Equations of Order 1< α<2 Abstract and Applied Analysis |
| title | The Solvability and Optimal Controls for Some Fractional Impulsive Equations of Order 1< α<2 |
| title_full | The Solvability and Optimal Controls for Some Fractional Impulsive Equations of Order 1< α<2 |
| title_fullStr | The Solvability and Optimal Controls for Some Fractional Impulsive Equations of Order 1< α<2 |
| title_full_unstemmed | The Solvability and Optimal Controls for Some Fractional Impulsive Equations of Order 1< α<2 |
| title_short | The Solvability and Optimal Controls for Some Fractional Impulsive Equations of Order 1< α<2 |
| title_sort | solvability and optimal controls for some fractional impulsive equations of order 1 α 2 |
| url | http://dx.doi.org/10.1155/2014/142067 |
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